Problem: A brand of cereal had $1.2$ milligrams $(\text{mg})$ of iron per serving. Then they changed their recipe so they had $1.8\,\text{mg}$ of iron per serving. What was the percent increase in iron?
Explanation: Let's start by finding the amount of increase in iron. $1.8\,\text{mg}-1.2\,\text{mg}=0.6\,\text{mg}$ What percent of $1.2$ milligrams is $0.6$ milligrams? We can rewrite that question as an equation. $\begin{array}{ccccc} {\text{what percent}}&\text{of}&{1.2\,\text{mg}}&\text{is}&0.6\,\text{mg}\\\\ {?\%}&\times &{1.2}&=&0.6 \end{array}$ Let's solve for the percent. $\begin{aligned} \dfrac{{?\%}\times {1.2}}{1.2}&=\dfrac{0.6}{1.2}\\\\ {?\%}&={0.5} \end{aligned}$ Percent means per hundred, so ${0.5}$ is equivalent to ${\dfrac{50}{100}}$ and also to ${50\%}$. There was a $50\%$ increase in iron.